1. Field of the Invention
The present invention is related to a method of measuring the three dimensional position of particles, in particular the velocity of particles in motion in a fluid medium.
2. Description of the Related Art
Several techniques to measure the three dimensional position of particles in a fluid, in particular the velocity of particles in a fluid, have been developed. The computations of the local velocities are obtained by analyzing the local motions of the particles.
The first family of techniques concern the methods based on Laser Doppler Velocimetry (LDV) wherein the fluid volume under test is illuminated by two coherent laser beams. The interference between the two beams creates a pattern with parallel fringes with a spatial frequency that is depending on the angle between the two propagation directions. When a particle is crossing the volume, it travels across the sequence of the light fringes and diffuses light proportionally to the local light intensity. Therefore, the diffused light is modulated by a frequency that is determined by the speed of the particle and the fringe spacing. The diffused light is detected and its frequency is computed in such a way that the speed of the particle is estimated. LDV technique gives an accurate measurement but measures the global velocity in one direction in a local region.
The second family concerns the techniques developed for Particle Intensity Velocimetry (PIV) wherein the volume under test is illuminated with a tin light sheet. This one is perpendicularly observed by a video camera that images the particles illuminated by the light sheet. The velocimetry is computed by analyzing the particle motion in sequences of images. The PIV is a two dimensional method and no information about motions parallel to the optical axis of the camera lens can be measured.
The third family concerns the so-called Photogrammetric methods wherein the illuminated volume under test is observed by several video cameras (2-4) with different viewing directions. The cameras are triggered in such a way that the images are recorded at the same time by the different cameras. The digitized images are processed and each particle is located in the different images. The relative positions of the particles in each image allow computing the three dimensional position of each particle. The three dimensional velocity maps are obtained by analyzing sequences of images. The main drawbacks of this system are:
The limited depth of view available with the classical imaging lenses. This becomes crucial when the volume of interest is small (typically less than 1 cm3).
The angles of viewing directions lead often to hidden parts of the volume of interest.
The fourth family is based on Digital holographic methods. In particular, a digital holographic method has been disclosed by Skarman, Wozniac and Becker, xe2x80x9cSimultaneous 3D-PIV and temperature measurement using a new CCD based holographic interferometerxe2x80x9d, Flow Meas. Instruction., Vol. 7, Nxc2x01, pp 1-6, 1996. This technique uses a digital refocus of the particle images. The optical set up is an interferometer. A laser beam (object beam) is transmitted through the volume under test and is imaged by a lens on the input face of a video camera. A second coherent beam is also incident on the input face of the camera. The two beams are interfering in such a way that the amplitude and the phase of the object beam can be computed by digital methods. As only one plane of the volume under test can be imaged, there is an important loss of information. However, the digital refocus allows to reconstruct the images of the particles.
The proposed method presents several drawbacks. First, due to a transmission illumination, only large particles can be considered. In the case of small particles, the disturbances of the optical field that they create are too weak to be measured with accuracy. Second, the computation of the optical phase is performed by the so-called phase stepping method. It requests to record several video frames with small changes of the optical paths introduced in the reference beam. This small changes of the optical paths takes time as the recording of the several video frames. During processing, the particles have to be sufficiently immobile in such a way that the method may only be used for low velocities. The three dimensional velocities are computed by analyzing sequences of images.
The last family concerns holographic methods using holographic recording media which can be thermoplastic films, silver halide films, etc. During the recording step, a hologram sequence of the moving particles is recorded. After processing, (thermal processing for thermoplastic, wet processing for the silver halide films), the holograms are reconstructed by illumination with a laser beam. The hologram is able to record the three dimensional information that can be measured with an imaging system like a video camera placed on a translation stage. Therefore the particle position measurements along the optical axis request mechanical motion of the imaging system.
This system presents several limitations. First, the holographic materials are always of weak sensitivity requesting a long exposure time or a high power laser. Secondly, the system needs a mechanical motion that is a source of positioning errors. Finally, the number of holograms that can be recorded in a sequence is limited. In practice, it is difficult to have more than 250 holograms.
The present invention aims to provide an improved digital holographic method for measuring the position of particles in a fluid medium, in particular for measuring the velocity of the particles. The method is able to refocus the image of the particles (seeds) moving in the fluid medium without the necessity of having several images being captured to get the complete three dimensional information, i.e., the amplitude and the phase.
More precisely, the present invention relates to a method which can be applied even to the measurement of the velocity of small and very small particles moving in fluid. With appropriate adjustments of the optical systems, the size range of the particles is typically from 500 xcexcm to 0.1 xcexcm.
Finally, the present invention concerns a method, which is able to measure the velocity of the fluid even if the speed of the particles is rather important. An estimation of the speed range of the particles is from 0 m/s to 600 w/s, where w is the size of the particles.
The present invention also relates to a method, which provides for improved speed processing, compared to most of the techniques of the state of the art.
Another aspect of the present invention is to provide an apparatus for performing said method.
Other advantages are described in the following detailed description.
The present invention is related to a method of measuring the three dimensional position of particles, possibly in motion, in a fluid medium contained in a sample by recording a digital hologram of said particles on an image sensor and by reconstructing the image of said particles from said hologram, the recording comprising:
providing a source beam with a coherent source;
generating at least two beams from said source beam, namely a reference beam and at least one object beam, said reference beam and said object beam being mutually coherent;
illuminating said sample by condensing said object beam onto said sample in order to obtain a scattered object beam for each particle;
transforming said scattered object beam into a spherical converging object beam toward said image sensor for each particle;
forming a diverging spherical beam from said reference beam;
superposing said spherical converging object beam for each particle and said diverging spherical beam on said image sensor, thereby obtaining on said image sensor an hologram of said particles by interfering said beams.
Preferably, said object beam is obtained by reflection of the source beam and said reference beam is obtained by transmission of the source beam.
In the case of the measurement of the velocity of a particle, the method further comprises the step of recording the time evolution of said hologram so that a sequence of holograms is obtained and the step of reconstructing a sequence of images from said sequence of holograms in order to determine the velocity of the particles in the fluid medium.
According to a preferred embodiment, the object beam is split into several object beams after being generated so that the illumination of the sample is performed with the object beams thus obtained.
In order to have the reconstruction of the image of the particles contained in the sample, the following acts are performed:
recording a reference hologram on the image sensor in the absence of the illuminating object beam and digitizing said reference hologram;
subtracting said digitized reference hologram to the digitized hologram of the particles which has been recorded in the presence of the illuminating object beam;
demodulating the resulting digitized hologram using the classical Fourier Transform method in order to obtain a Fourier Transform function depicting the three dimensional positions of the particles;
filtering said Fourier Transform function; and
calculating an inverse Fourier Transform function from said filtered Fourier Transform function thus obtained.
In order to have the reconstruction of the sequence of images of the particles contained in the sample as a function of time, the following acts are performed:
recording a sequence of reference holograms on the image sensor in the absence of the illuminating object beam and digitizing said sequence of reference holograms;
subtracting said sequence of reference holograms to the sequence of holograms of the particles which has been recorded in the presence of the illuminating object beam and digitized;
demodulating the resulting sequence of holograms using the classical Fourier Transform method in order to obtain a sequence of Fourier Transform functions depicting the evolution of the three dimensional positions of the particles according time;
filtering said sequence of Fourier Transform functions; and
calculating a sequence of inverse Fourier Transform functions from said sequence of filtered Fourier Transform functions thus obtained.
A preferred embodiment also relates to an apparatus for measuring the three dimensional position or the velocity of the particles, preferably in motion, in a fluid contained in a sample, wherein the apparatus comprises:
a coherent source able to generate a coherent source beam;
means for generating at least two coherent beams from said source beam, namely a reference beam and at least one object beam;
an image sensor;
means for condensing said object beam onto said sample in order to obtain a scattered object beam;
means for transforming said scattered object beam into a spherical converging object beam for each particle on said image sensor; and
means for forming a diverging spherical beam from said reference beam on said image sensor.
According to a preferred embodiment, the means for transforming said scattered object beam into the spherical converging object beam for each particle on said image sensor are consisting in an afocal device essentially comprising a microscope lens and another lens.
Preferably, said afocal device is associated with an aperture whose maximum size, preferably the diameter, is adjustable in order to match the resolution of the afocal device and the resolution of the image sensor.
Advantageously, the coherent source is a laser source and the means for generating the reference beam and at least one object beam are consisting in a first beam splitter placed behind said laser source.
Preferably, the means for condensing said object beam onto said sample in order to obtain a scattered object beam are a condensing lens.
According to another preferred embodiment, the means for condensing said object beam onto said sample in order to obtain a scattered object beam are essentially consisting in the afocal device associated with a polarizing beam splitter which is combined to a wave plate for achieving optical insulation of the object beam. Preferably, there is also a polariser.
Preferably, the means for forming the diverging spherical beam from the reference beam on said image sensor are essentially consisting in a beam splitter.
According to another embodiment, the means for generating the reference beam and at least one object beam are consisting in an optical fiber coupler placed behind said laser source.
Preferably, in this case, the means for condensing the object beam onto said sample in order to obtain a scattered object beam are a monomode optical fiber coupled to the optical fiber coupler.
Preferably, in this case, the means for forming the diverging spherical beam from the reference beam on said image sensor are essentially consisting in a monomode optical fiber coupled to the optical fiber coupler.
Preferably, the apparatus also comprises means for recording and digitizing interference patterns as functions of time and means for treating said digitized interference patterns.
Advantageously, said means for recording and digitizing the interference patterns are classical hologram supports, and more preferably a CCD camera coupled with computing means.
Advantageously, the apparatus also comprises means for splitting the object beam into several object beams able to illuminate the sample.
The study of particle-particle interactions in aerosols, the control of protein crystal growth or the control of the state of samples in space are examples of potential applications of the method according to the invention.